Money Must be Paid in Marriage

Question :

Is it permissible for the Muslim to give his daughter in marriage to a man for Allah's sake, and not to take a dowry for it?

Answer:

Money must be present in case of marriage, according to the Words of Allah, Most Glorified, Most High:
"All others are lawful, provided you seek (them in marriage) with Mahr (bridal-money given by the husband to his wife at the time of marriage) from your property."

and the words of the Prophet in the Hadith of Sahl bin Sa'd, may Allah be pleased with him, whose authenticity is agreed upon (by Imams Al-Bukhari and Muslim) to the one who proposed marriage to a woman who offered herself to the Prophet SAW:
"Search for something, even if it is only an iron ring."

When a man marries a woman without a dowry, then the woman must be given a substitute for a monetary dowry: It is permissible (for example,) to marry a woman on the under- standing that he will teach her something from the Qur'an or Hadith, or some kind of useful knowledge. This is because the Prophet married the aforementioned suitor to the woman who offered herself to him, on the understanding that he would teach her something from the Qur'an, when he could not find any wealth. The dowry is a woman's right; but when she waives this right, if she is of sound mind and of full legal age, that is correct, according to the Words of Allah, the Almighty, the All- Powerful:
"And give to the women (whom you marry) their Mahr (obligatory bridal-money given by the husband to his wife at the time of marriage) with a good heart."

Source:
Ibn Baz
Fatawa Islamiyah, Vol. 5 Pages 304-305